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arXiv · 2312.14642

Adjoints of sums of m-accretive operators and applications to non-autonomous evolutionary equations

Rainer Picard·Sascha Trostorff·Marcus Waurick
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Abstract

We provide certain compatibility conditions for m-accretive operators such that the adjoint of the sum is given by the closure of the sum of the respective adjoint. We revisit the proof of well-posedness of the abstract class of partial differential-algebraic equations known as evolutionary equations. We show that the general mechanism provided here can be applied to establish well-posedness for non-autonomous evolutionary equations with $L_{\infty}$-coefficients thus not only generalising known results but opening up new directions other methods such as evolution families have a hard time to come by.

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Rainer Picard, Sascha Trostorff, Marcus Waurick. 2023-12-22. Adjoints of sums of m-accretive operators and applications to non-autonomous evolutionary equations. https://arxiv.org/abs/2312.14642

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